TNL::Solvers::Linear Namespace Reference

Namespace for linear system solvers. More...

Namespaces
namespace	Preconditioners
	Namespace for preconditioners of linear system solvers.

Classes
class	BICGStab
	Iterative solver of linear systems based on the biconjugate gradient stabilized (BICGStab) method. More...
class	BICGStabL
	Iterative solver of linear systems based on the BICGStab(l) method. More...
class	CG
	Iterative solver of linear systems based on the conjugate gradient method. More...
class	GMRES
	Iterative solver of linear systems based on the Generalized minimal residual (GMRES) method. More...
class	Jacobi
	Iterative solver of linear systems based on the Jacobi method. More...
struct	LinearResidueGetter
class	LinearSolver
	Base class for iterative solvers of systems of linear equations. More...
class	SOR
	Iterative solver of linear systems based on the Successive-overrelaxation (SOR) or Gauss-Seidel method. More...
class	TFQMR
	Iterative solver of linear systems based on the Transpose-free quasi-minimal residual (TFQMR) method. More...
struct	Traits
struct	Traits< Matrices::DistributedMatrix< Matrix > >

Functions
template<bool fullStorage = true, typename Matrix , typename Vector1 , typename Vector2 >
void	triangularSolveLower (const Matrix &L, Vector1 &x, const Vector2 &b)
template<bool reversedRows = false, bool fullStorage = true, typename Matrix , typename Vector1 , typename Vector2 >
void	triangularSolveUpper (const Matrix &U, Vector1 &x, const Vector2 &b)

Detailed Description

Namespace for linear system solvers.

This namespace contains the following algorithms and methods for solution of linear systems.

Direct methods

Iterative methods

Stationary methods

1. Jacobi method - TNL::Solvers::Linear::Jacobi
2. Successive-overrelaxation method, SOR - TNL::Solvers::Linear::SOR

Krylov subspace methods

1. Conjugate gradient method, CG - TNL::Solvers::Linear::CG
2. Biconjugate gradient stabilized method, BICGStab - TNL::Solvers::Linear::BICGStab
3. BICGStab(l) method - TNL::Solvers::Linear::BICGStabL
4. Transpose-free quasi-minimal residual method, TFQMR - TNL::Solvers::Linear::TFQMR
5. Generalized minimal residual method, GMERS - TNL::Solvers::Linear::GMRES with various methods of orthogonalization
   1. Classical Gramm-Schmidt, CGS
   2. Classical Gramm-Schmidt with reorthogonalization, CGSR
   3. Modified Gramm-Schmidt, MGS
   4. Modified Gramm-Schmidt with reorthogonalization, MGSR
   5. Compact WY form of the Householder reflections, CWY